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US Airways periodically puts its miles on sale at very good prices after bonuses. Those miles can currently be redeemed on UA and US. Eventually, when the AA/US merger is completed, the miles should be redeemable on AA (and possible on AS and HA too, as those carriers are AA partners).
BA Avios are redeemable on AA flights, at BA's redemption rates. Once AA starts CMH-LAX nonstop service in August, CMH-LAX-Hawaii should be bookable for 22,500 Avios one way. And BA would permit a stopover of any length at LAX.